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3.d. Intensity of convection (2): Conduction layer
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Vertical gradient of potential temperature below about 50
m height shows good agreement
with that described by turbulent diffusion.
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(2) |
where  is heat flux.
In evaluating (2), we have adopted = 30
Wm-2 obtained from the total amount
of infrared radiative heating and sensible heat flux at
around noon,
ρ0 =
2×10-2
kgm-3,  = 734.9
Jkg-1
K-1, and  = 15
m2sec-1
obtained from the value of turbulent diffusion
coefficient calculated in our numerical model.
The region below about 50 m height in the thermal boundary
layer can be referred to as the conduction layer.
Provided that the temperature structure of the conduction
layer is given by (2),
let us estimate the depth of conduction layer  and
potential temperature difference  of the layer.
The flux Rayleigh number of the conduction layer is given as
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(3) |
where  is thermal expansion
coefficient,  is gravitational
acceleration,  is temperature flux
( ), κ and ν
are thermal diffusion coefficient and kinematic
viscosity, respectively.
Convective instability is expected to appear
when the flux Rayleigh number exceeds the critical value.
Supposing that κ = ν = and = 1/
 , the depth of the conduction
layer can be estimated by using (2)
as
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(4) |
According to linear stability analysis, the order of
magnitude of the critical Rayleigh number is about 100
under fixed heat flux boundary condition (Sasaki, 1970).
Substituting this, we obtain ˜
57 m, and from (2),
we have
˜ 8 K.
Although the values of conduction layer thickness and potential
temperature difference at LT = 14:00 shown in Figure 7
( < 50 m, ˜ 6 K)
are slightly smaller
than those obtained above,
they are fairly acceptable as order estimations.
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